We are asked to find the length of LM. Let's consider the diagram.
As we can see, LM consists of two segments: MF and FL. According to the Segment Addition Postulate, its length equals the sum of these smaller segment lengths.
LM= MF+ FL
The length of MF is known from the diagram but how can we find the length of FL? From the diagram, we see that JM and JL have the same length. This means point J is equidistant from M and L. Let's now use the Converse of the Perpendicular Bisector Theorem.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
According to the theorem, JF is the perpendicular bisector of ML. Therefore, point F is the midpoint of ML. From here, we can conclude that the length of LF is also 6. Finally, we can substitute MF= 6 and FL= 6 into the equation to find LM.
LM= 6+ 6=12
